Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 356 / 2 / e

Under the independence closure, the mean rightward flux across the bond $(i,i+1)$ isThe mean equation is the discrete conservation law ${\dot{M}}_i=J_{i-1/2}-J_{i+1/2}$. Substitution of the rates from part c and Taylor expansion show that the exclusion factors cancel from the symmetric diffusive contribution but remain in the biased contribution:Therefore the mean-field asymmetric simple exclusion process limit isThe factor $1-c$ is the probability that the destination site is vacant.